B-spline Finite Element Method Applied to Boundary Value Problem and Convergence Rate Analysis

This paper adopts the open uniform B-spline functions as finite element interpolation functions to solve the boundary value problem. It compares the numerical solutions of the B-spline finite element method with those of the Lagrange finite element method. The convergence rate of the B-spline solutions is better than that of the Lagrange method, and the results of the B-spline were continuous, whereas those of the Lagrange method were discontinuous. Consequently, when high accuracy numerical solutions are required, the B-spline finite element methods are less time-consuming than the Lagrange method.